Nonuniform fast Fourier transforms with nonequispaced spatial and frequency data and fast sinc transforms

TL;DR

This paper introduces an efficient algorithm for the nonuniform fast Fourier transform with nonuniform data in both space and frequency, utilizing window functions to achieve exponential error decay, and applies it to the fast sinc transform.

Contribution

It develops a novel NNFFT algorithm with sinh-type window functions and demonstrates its exponential accuracy, also applying it to improve the fast sinc transform.

Findings

Error decays exponentially with truncation parameters.

The NNFFT algorithm effectively handles nonuniform data.

Fast sinc transform accuracy is also improved.

Abstract

In this paper we study the nonuniform fast Fourier transform with nonequispaced spatial and frequency data (NNFFT) and the fast sinc transform as its application. The computation of NNFFT is mainly based on the nonuniform fast Fourier transform with nonequispaced spatial nodes and equispaced frequencies (NFFT). The NNFFT employs two compactly supported, continuous window functions. For fixed nonharmonic bandwidth, it is shown that the error of the NNFFT with two sinh-type window functions has an exponential decay with respect to the truncation parameters of the used window functions. As an important application of the NNFFT, we present the fast sinc transform. The error of the fast sinc transform is estimated as well.